AFAIK, metho will not mix well with oil based paint.

As for turps & the artist's oil paint on the veneer, I'm going to go out on limb and say it would be no different than using an oil based stain like Feast Watson, and plenty of people have done that without issue.

Not sure why you need the BLO in the mix. I know artists do that when painting on canvas, but I thought that was about texture/consistency as well as acting as a drying retarder. I don't know where that came from as I have never done an oil painting in my life.

Light applications of a spirit or oil based stain/dye (or even water based for that matter) won't be a problem on veneer unless you absolutely saturated it. Then maybe it could have an effect on the adhesive.